Options dan Futures DWITYAPOETRA S. BESAR MATA KULIAH : ANALISIS INVESTASI DAN MANAJEMEN RISIKO 2013 PROG STUDI MAGISTER MANAJEMEN UNIVERSITAS TRISAKTI
Bahan Bodie, Kane, and Marcus (BKM), 2009, Investments, 8 th (global) edition, McGraw-Hill / Irwin. Kuliah sesi ini: BKM, Bab 20, 21 dan 22 Soal:
Outline Bagian 1: Pasar Opsi Bagian 2: Valuasi Opsi Bagian 3: Pasar Futures
Bagian 1: Pasar Opsi
Terminologi Opsi Buy - Long Sell - Short Call Put Key Elements Exercise atau Strike Price Premium atau Price Maturity atau Expiration
Pasar Opsi Hubungan harga pasar dan eksekusi In the Money - exercise of the option would be profitable Call: market price>exercise price Put: exercise price>market price Out of the Money - exercise of the option would not be profitable Call: market price<exercise price Put: exercise price<market price At the Money - exercise price and asset price are equal
Opsi Tabel Opsi saham IBM
Opsi American vs. European Options American - the option can be exercised at any time before expiration or maturity European - the option can only be exercised on the expiration or maturity date
Opsi Jenis Opsi Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options
Opsi Payoffs and Profits at Expiration - Calls Notation Stock Price = S T Exercise Price = X Payoff to Call Holder (S T - X) if S T >X 0 if S T < X Profit to Call Holder Payoff - Purchase Price
Opsi - Calls Payoffs and Profits at Expiration - Calls Payoff to Call Writer - (S T - X) if S T >X 0 if S T < X Profit to Call Writer Payoff + Premium
Opsi Grafik Payoff dan Profit to Call Option saat Expiration
Opsi Grafik Payoff dan Profit to Call Writers saat Expiration
Opsi - Puts Payoffs and Profits at Expiration - Puts Payoffs to Put Holder 0 if S > X T (X - S ) if S < X T T Profit to Put Holder Payoff - Premium
Opsi Payoffs and Profits at Expiration Puts Continued Payoffs to Put Writer 0 if S T > X -(X - S T ) if S T < X Profits to Put Writer Payoff + Premium
Opsi Strategi Opsi Straddle (Same Exercise Price) Long Call and Long Put Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration. Vertical or money spread: Same maturity Different exercise price Horizontal or time spread: Different maturity dates
Opsi Table 20.3 Value of a Straddle Position at Option Expiration
Opsi If the prices are not equal arbitrage will be possible Put Call Parity X C S P 0 r (1 ) T f
Opsi Contoh Put Call Parity - Disequilibrium Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 5% Maturity = 1 yr X = X105 C S0 P (1 r ) T f 117 > 115 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative
Opsi Tabel Strategi Arbitrasi
Opsi Sekuritas yang mirip Opsi Callable Bonds Convertible Securities Warrants Collateralized Loans
Opsi Exotic Options Asian Options Barrier Options Lookback Options Currency Translated Options Digital Options
Outline Bagian 2: Valuasi Opsi
Valuasi Opsi Nilai intrinsic (Intrinsic value) - profit that could be made if the option was immediately exercised Call: stock price - exercise price Put: exercise price - stock price Nilai waktu - the difference between the option price and the intrinsic value
Valuasi Opsi Grafik Call Option Value sebelum Expiration
Valuasi Opsi Tabel Faktor Determinan Nilai Call Option
Valuasi Opsi Restriksi pada nilai opsi : Call Value cannot be negative Value cannot exceed the stock value Value of the call must be greater than the value of levered equity C > S 0 - ( X + D ) / ( 1 + r f ) T C > S 0 - PV ( X ) - PV ( D )
Valuasi Opsi Grafik Range of Possible Call Option Values
Valuasi Opsi Grafik Call Option Value as a Function of the Current Stock Price
Valuasi Opsi Contoh: Binomial Option Pricing 120 10 100 C 90 0 Stock Price Call Option Value X = 110
Valuasi Opsi Binomial Option Pricing: Alternative Portfolio Buy 1 share of stock at $100 Borrow $81.82 (10% Rate) Net outlay $18.18 Payoff Value of Stock 90 120 Repay loan - 90-90 Net Payoff 0 30 18.18 30 0 Payoff Structure is exactly 3 times the Call
Valuasi Opsi Binomial Option Pricing: 30 30 18.18 C 0 0 3C = $18.18 C = $6.06
Valuasi Opsi Expanding to Consider Three Intervals: Assume that we can break the year into three intervals For each interval the stock could increase by 5% or decrease by 3% Assume the stock is initially selling at 100
Valuasi Opsi Expanding to Consider Three Intervals Continued S + + S + + + S + S + + - S S - S + - S - - S + - - S - - -
Valuasi Opsi Possible Outcomes with Three Intervals Event Probability Final Stock Price 3 up 1/8 100 (1.05) 3 =115.76 2 up 1 down 3/8 100 (1.05) 2 (.97) =106.94 1 up 2 down 3/8 100 (1.05) (.97) 2 = 98.79 3 down 1/8 100 (.97) 3 = 91.27
Valuasi Opsi Valuasi dengan model Black-Scholes C o = S o N(d 1 ) - Xe -rt N(d 2 ) d 1 = [ln(s o /X) + (r + 2 /2)T] / ( T 1/2 ) d 2 = d 1 + ( T 1/2 ) where C o = Current call option value S o = Current stock price N(d) = probability that a random draw from a normal distribution will be less than d
Valuasi Opsi Black-Scholes Option Valuation X = Exercise price e = 2.71828, the base of the natural log r = Risk-free interest rate (annualizes continuously compounded with the same maturity as the option) T = time to maturity of the option in years ln = Natural log function Standard deviation of annualized cont. compounded rate of return on the stock
Valuasi Opsi Grafik Kurva Distribusi Normal
Valuasi Opsi Contoh Call Option: S o = 100 X = 95 r =.10 T =.25 (quarter) =.50 d 1 = [ln(100/95) + (.10+( 5 2 /2))] / ( 5.25 1/2 ) =.43 d 2 =.43 + (( 5.25 1/2 ) =.18
Valuasi Opsi Probabilities dari Distribusi Normal N (.43) =.6664 Table 21.2 d N(d).42.6628.43.6664 Interpolation.44.6700
Valuasi Opsi Probabilities from Normal Distribution Continued N (.18) =.5714 Table 21.2 d N(d).16.5636.18.5714.20.5793
Valuasi Opsi Tabel Cumulative Normal Distribution
Valuasi Opsi Nilai Opsi Call C o = S o N(d 1 ) - Xe -rt N(d 2 ) C o = 100 X.6664-95 e -.10 X.25 X.5714 C o = 13.70 Implied Volatility Using Black-Scholes and the actual price of the option, solve for volatility. Is the implied volatility consistent with the stock?
Valuasi Opsi Contoh Spreadsheet utk menghitung nilai opsi Black-Scholes
Valuasi Opsi Menggunakan Goal Seek utk mendapatkan Implied Volatility
Valuasi Opsi Grafik Implied Volatility of the S&P 500 (VIX Index)
Valuasi Opsi Black-Scholes Model dengan Dividend The call option formula applies to stocks that pay dividends One approach is to replace the stock price with a dividend adjusted stock price Replace S 0 with S 0 - PV (Dividends)
Valuasi Opsi Put Value Using Black-Scholes P = Xe -rt [1-N(d 2 )] - S 0 [1-N(d 1 )] Using the sample call data S = 100 r =.10 X = 95 g =.5 T =.25 95e -10x.25 (1-.5714)-100(1-.6664) = 6.35
Valuasi Opsi Put Option Valuation: Using Put-Call Parity P = C + PV (X) - S o = C + Xe -rt - S o Using the example data C = 13.70 X = 95 S = 100 r =.10 T =.25 P = 13.70 + 95 e -.10 X.25-100 P = 6.35
Valuasi Opsi Using the Black-Scholes Formula Hedging: Hedge ratio or delta The number of stocks required to hedge against the price risk of holding one option Option Elasticity Call = N (d 1 ) Put = N (d 1 ) - 1 Percentage change in the option s value given a 1% change in the value of the underlying stock
Valuasi Opsi Portfolio Insurance Buying Puts - results in downside protection with unlimited upside potential Limitations Tracking errors if indexes are used for the puts Maturity of puts may be too short Hedge ratios or deltas change as stock values change
Valuasi Opsi Hedging On Mispriced Options Option value is positively related to volatility: If an investor believes that the volatility that is implied in an option s price is too low, a profitable trade is possible Profit must be hedged against a decline in the value of the stock Performance depends on option price relative to the implied volatility
Valuasi Opsi Hedging dan Delta The appropriate hedge will depend on the delta Recall the delta is the change in the value of the option relative to the change in the value of the stock Delta = Change in the value of the option Change of the value of the stock
Outline Bagian 3: Pasar Futures
3. Pasar Futures Futures dan Forwards Forward - an agreement calling for a future delivery of an asset at an agreed-upon price Futures - similar to forward but feature formalized and standardized characteristics Key difference in futures Secondary trading - liquidity Marked to market Standardized contract units Clearinghouse warrants performance
3. Pasar Futures Key Terms untuk Futures Contracts Futures price - agreed-upon price at maturity Long position - agree to purchase Short position - agree to sell Profits on positions at maturity Long = spot minus original futures price Short = original futures price minus spot
3. Pasar Futures Tabel Futures Listing
3. Pasar Futures Grafik Profits to Buyers and Sellers of Futures and Option Contracts
3. Pasar Futures Tabel Contoh Kontrak Future
3. Pasar Futures Clearinghouse - acts as a party to all buyers and sellers Obligated to deliver or supply delivery Closing out positions Reversing the trade Take or make delivery Most trades are reversed and do not involve actual delivery Open Interest Trading Mechanics
3. Pasar Futures Skema Panel A, Trading without a Clearinghouse. Panel B, Trading with a Clearinghouse
3. Pasar Futures Margin and Trading Arrangements Initial Margin - funds deposited to provide capital to absorb losses Marking to Market - each day the profits or losses from the new futures price are reflected in the account Maintenance or variation margin - an established value below which a trader s margin may not fall
3. Pasar Futures Margin and Trading Arrangements Continued Margin call - when the maintenance margin is reached, broker will ask for additional margin funds Convergence of Price - as maturity approaches the spot and futures price converge Delivery - Actual commodity of a certain grade with a delivery location or for some contracts cash settlement Cash Settlement some contracts are settled in cash rather than delivery of the underlying assets
3. Pasar Futures Strategi Perdagangan Speculation - short - believe price will fall long - believe price will rise Hedging - long hedge - protecting against a rise in price short hedge - protecting against a fall in price
3. Pasar Futures Basis dan Basis Risk Basis - the difference between the futures price and the spot price over time the basis will likely change and will eventually converge Basis Risk - the variability in the basis that will affect profits and/or hedging performance
3. Pasar Futures 3. Pasar Futures Grafik Hedging Revenues Using Futures (Futures Price = $97.15)
3. Pasar Futures Harga Futures Spot-futures parity theorem - two ways to acquire an asset for some date in the future Purchase it now and store it Take a long position in futures These two strategies must have the same market determined costs
3. Pasar Futures Spot-Futures Parity Theorem With a perfect hedge the futures payoff is certain -- there is no risk A perfect hedge should return the riskless rate of return This relationship can be used to develop futures pricing relationship
3. Pasar Futures Contoh Hedge : Investor owns an S&P 500 fund that has a current value equal to the index of $1,500 Assume dividends of $25 will be paid on the index at the end of the year Assume futures contract that calls for delivery in one year is available for $1,550 Assume the investor hedges by selling or shorting one contract
3. Pasar Futures Contoh Hedge Value of S T 1,510 1,550 1,610 Payoff on Short (1,550 - S T ) 40 0-60 Dividend Income 25 25 25 Total 1,575 1,575 1,575
3. Pasar Futures Rate of Return for the Hedge ( F 0 D) S S 0 (1,550 25) 1,500 1,500 0 5%
3. Pasar Futures General Spot-Futures Parity F ( F D S 0 ) 0 S 0 r f Rearranging terms 0 S0(1 rf ) D S0(1 rf d) d D S 0
3. Pasar Futures Kemungkinan melakukan Arbitrasi If spot-futures parity is not observed, then arbitrage is possible If the futures price is too high, short the futures and acquire the stock by borrowing the money at the risk free rate If the futures price is too low, go long futures, short the stock and invest the proceeds at the risk free rate
Spread Pricing: Parity for Spreads 1 2 1 2 0 1 0 2 ) ( 2 1 (1 ) ( ) (1 ) ( ) ( ) ( )(1 ) T f T f T T f r d F S T r d F S T r d F F T T 3. Pasar Futures
3. Pasar Futures Teori Harga Futures Expectations Normal Backwardation Contango Modern Portfolio Theory
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